Question

giải phương trình sau ;

\(\sqrt{x-\sqrt{1-x}}\) + \(\sqrt{x}\) = 2

Answer 1

\(\sqrt{x-\sqrt{1-x}}+\sqrt{x}=2\)
\(\Leftrightarrow\sqrt{x^2-\left(\sqrt{\left(1-x\right)^2}\right)^2}+\sqrt{x^2}=2\)
\(\Leftrightarrow x-1+x+x=2\)
\(\Leftrightarrow3x-1=2\)
\(\Leftrightarrow3x=3\)
\(\Leftrightarrow x=1\)

Answer 2

\(\sqrt{x-\sqrt{ }1-x}+\sqrt{x}=2 \)
\(\Leftrightarrow\sqrt{x^2-\sqrt{\left(1-x\right)^2}}+\sqrt{x^2}=2\)
\(\Leftrightarrow x-1+x+x=2\)
\(\Leftrightarrow3x-1=2\)
\(\Leftrightarrow3x=3\)
\(\Leftrightarrow x=1\)